Direct numerical computation of periodic orbits and their stability

Williams, P 2006, 'Direct numerical computation of periodic orbits and their stability', Journal of Spacecraft and Rockets, vol. 43, no. 5, pp. 1143-1146.


Document type: Journal Article
Collection: Journal Articles

Title Direct numerical computation of periodic orbits and their stability
Author(s) Williams, P
Year 2006
Journal name Journal of Spacecraft and Rockets
Volume number 43
Issue number 5
Start page 1143
End page 1146
Total pages 4
Publisher American Institute of Aeronautics and Astronautics
Abstract A numerical approach for directly computing periodic orbits and their corresponding stability through Legendre pseudospectral methods is presented. The method is able to generate periodic orbits without continuation, and is applicable to natural and forced periodic orbits. The approach relates the Jacobian of the discretized equations used in the determination of the periodic orbits to the monodromy matrix, which yields the stability information. It is possible to obtain numerical solutions for uncontrolled and optimally controlled periodic processes with this approach. The approach is also helpful in assessing the stability of the solutions without any formal derivations of the necessary conditions. This makes stability computations very efficient and effective for complex systems for which analytic derivatives may be difficult to construct.
Subject Satellite, Space Vehicle and Missile Design and Testing
Keyword(s) pseudospectral method
optimal cruise
optimization
algorithm
vehicle
flight
DOI - identifier 10.2514/1.20930
Copyright notice Copyright © 2006 by Paul Williams
ISSN 0022-4650
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